The Hammers are yet to receive an offer for the wantaway striker, who has grown increasingly frustrated at being unable to break into the first team at Upton Park
Vaz Te, who has voiced his frustration at a lack of first-team football has handed in a transfer request at Upton Park.
Allardyce revealed the Premier League club have not received any bids for the 26-year-old, but expects interest before the transfer window closes on Monday.
"He might leave now, if anybody's going to leave now it would be Vaz," he told reporters. "You don't keep anybody that doesn't want to stay.
"If a club comes and makes the right offer for him then we would be more than happy to accommodate the transfer request he's given us.
"We've had no offers yet but I'd expect that we have an enquiry for him in the next couple of days.
"If he wants to leave, he can. But the offer has to be right for us."
Vaz Te made his first start of the season in the midweek Capital One Cup victory over Cheltenham Town scoring in the process.
However, it was Ravel Morrison - who also got on the scoresheet - who drew the plaudits from Allardyce.
"Ravel's performance on Tuesday was a carry on from his pre-season and we were all delighted with it, particularly the goal," he added.
"With six (goals) in pre-season and another on Tuesday it's making a real statement."